Lesson 1
Key Topics
- Caesar Cipher / Frequency Analysis (Recap)
- Polygraphic Cipher
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Caesar Cipher / Frequency Analysis
Okay, the Caesar Cipher is all the way back over here and what you should remember about frequency analysis is found here. However, as it's highly probable you have no memory of them and are like me and lazy, here's the review!
- The Caesar Cipher involves shifting the alphabet along. For example a shift of 3 would look like:
- Frequency analysis compares the distribution of letters (how many of each) in the ciphertext with the standard distribution of letters in the English language. For example, in the plaintext, a peak is typically seen for the letter "E" (see the typical frequency distribution chart for letters given below).
- The shift can be identified by matching the "peaks" in the distributions.
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Polygraphic Cipher
The polygraphic, (one-to-many) cipher aims to flatten the frequency distribution of the ciphertext letters, thus defeating frequency analysis. An example of a polygraphic cipher where each plaintext letter becomes a 2-digit number is given below.
It can also be seen in *this Googledocs spreadsheet*.
The polygraphic, (one-to-many) cipher aims to flatten the frequency distribution of the ciphertext letters, thus defeating frequency analysis. An example of a polygraphic cipher where each plaintext letter becomes a 2-digit number is given below.
It can also be seen in *this Googledocs spreadsheet*.
The most common letters are assigned more numbers in the cipher as they are more likely to occur. For example the word: AND could be represented as any of the following (and many more combinations): 38 11 75 or 33 54 81 or 04 98 75.
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Assignment 1
- Due: end of 31st May 2012
- All work is OPTIONAL (of the optional work you must complete any 10 questions for full points - see the Points Breakdown for more details)
- Up to 50 points total.
- Complete either one or both questions. If you want to only do one question to start and another later that's fine, you can send them separately. However, please do send each question fully completed (i.e. I don't want Q1A in one e-mail and Q1B in another).
- Send to: [email protected]
- E-mail subject: CC2-1-HOL ID (replace HOL ID with your HOL ID, for example I could put: CC2-1-ma607)
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Q1. (25 points total)
A) Fill in the blanks. 5 points.
The polygraphic cipher can also be called a ___-__-____ cipher. It ________ the frequency _________ which prevents the decoder from using ________ analysis.
B) 5 points.
Identify the 4 most commonly used letters in the English language according to the frequency distribution chart given in the lesson.
C) Polygraphic cipher. 15 points.
Plaintext: SATURDAY AT MIDNIGHT, TOP OF ASTRONOMY TOWER.
Q2. (25 points total)
This question does not include polygraphic substitution, it instead focuses on frequency analysis by itself.
Two different ciphers have been used to encode the same plaintext. Cipher 1 created Ciphertext 1 and Cipher 2 led to Ciphertext 2. Both Cipher 1 and Cipher 2 are random monoalphabetic substitution ciphers - they are not Caesar or Atbash ciphers etc, the alphabet was all jumbled up to create the cipher.
Ciphertext 1: YD ZGT XTC HID HLW FHX ZGHU XTC PDDS YDMHCFD UGTFD ZGT BELW WTLU BHUUDI HLW UGTFD ZGT BHUUDI WTLU BELW
Ciphertext 2: YT SNA BAR OUT OHM SOB SNOE BAR LTTF YTIORWT ENAWT SNA DCHM MAHE DOEETU OHM ENAWT SNA DOETTU MAHE DCHM
A) Decode one of the two ciphertexts to discover the plaintext. (15 points)
I would suggest using logic/strategy as oppposed to frequency analysis and will give you the following hint: the word 'and' appears more than once.
B) Frequency analysis (10 points)
Create table(s) or graph(s) of the frequency distributions of the letters in the plaintext, ciphertext 1 and ciphertext 2. Compare the frequency distributions of ciphertext 1 and the plaintext; now of ciphertext 2 and the plaintext. What do you notice? One of the two ciphers was created in a less random manner than the other - can you see how?
For Q2 your e-mail should include: the decoded plaintext, the frequency distribution table(s)/graph(s), answers/discussion of the points mentioned.
A) Fill in the blanks. 5 points.
The polygraphic cipher can also be called a ___-__-____ cipher. It ________ the frequency _________ which prevents the decoder from using ________ analysis.
B) 5 points.
Identify the 4 most commonly used letters in the English language according to the frequency distribution chart given in the lesson.
C) Polygraphic cipher. 15 points.
Plaintext: SATURDAY AT MIDNIGHT, TOP OF ASTRONOMY TOWER.
- Encode the plaintext using a Caesar cipher (plaintext A--> ciphertext B).
- Encode the plaintext using the polygraphic cipher given in the lesson above. Do not repeat any numbers unless you have to.
- Did you have to use any numbers more than once?
- Discuss what the frequency distribution chart would look like for the Caesar cipher ciphertext compared with for the polygraphic cipher ciphertext. Why are they different? (For the polygraphic ciphertext obviously, you'd be having the numbers along the x-axis instead of the letters of the alphabet).
- You do not have to create the frequency distribution charts/tables.
Q2. (25 points total)
This question does not include polygraphic substitution, it instead focuses on frequency analysis by itself.
Two different ciphers have been used to encode the same plaintext. Cipher 1 created Ciphertext 1 and Cipher 2 led to Ciphertext 2. Both Cipher 1 and Cipher 2 are random monoalphabetic substitution ciphers - they are not Caesar or Atbash ciphers etc, the alphabet was all jumbled up to create the cipher.
Ciphertext 1: YD ZGT XTC HID HLW FHX ZGHU XTC PDDS YDMHCFD UGTFD ZGT BELW WTLU BHUUDI HLW UGTFD ZGT BHUUDI WTLU BELW
Ciphertext 2: YT SNA BAR OUT OHM SOB SNOE BAR LTTF YTIORWT ENAWT SNA DCHM MAHE DOEETU OHM ENAWT SNA DOETTU MAHE DCHM
A) Decode one of the two ciphertexts to discover the plaintext. (15 points)
I would suggest using logic/strategy as oppposed to frequency analysis and will give you the following hint: the word 'and' appears more than once.
B) Frequency analysis (10 points)
Create table(s) or graph(s) of the frequency distributions of the letters in the plaintext, ciphertext 1 and ciphertext 2. Compare the frequency distributions of ciphertext 1 and the plaintext; now of ciphertext 2 and the plaintext. What do you notice? One of the two ciphers was created in a less random manner than the other - can you see how?
For Q2 your e-mail should include: the decoded plaintext, the frequency distribution table(s)/graph(s), answers/discussion of the points mentioned.